Tournament-based harmony search algorithm for non-convex economic load dispatch problem

This paper proposes a tournament-based harmony search (THS) algorithm for economic load dispatch (ELD) problem. The THS is an efficient modified version of the harmony search (HS) algorithm where the random selection process in the memory consideration operator is replaced by the tournament selection process to activate the natural selection of the survival-of-the-fittest principle and thus improve the convergence properties of HS. The performance THS is evaluated with ELD problem using five different test systems: 3-units generator system; two versions of 13-units generator system; 40-units generator system; and large-scaled 80-units generator system. The effect of tournament size (t) on the performance of THS is studied. A comparative evaluation between THS and other existing methods reported in the literature are carried out. The simulation results show that the THS algorithm is capable of achieving better quality solutions than many of the well-popular optimization methods.     

VARIANCE-BASED HARMONY SEARCH ALGORITHM FOR UNIMODAL AND MULTIMODAL OPTIMIZATION PROBLEMS WITH APPLICATION TO CLUSTERING

This article presents a novel variance-based harmony search algorithm (VHS) for solving optimization problems. VHS incorporates the concepts borrowed from the invasive weed optimization technique to improve the performance of the harmony search algorithm (HS). This eliminates the main problem of constant parameter setting in the algorithm proposed recently and named as explorative HS. It uses the variance of a current population as well as presents a solution vector to improvise the harmony memory. In addition, the dynamic pitch adjustment operator is used to avoid solution oscillation. The proposed algorithm is evaluated on 14 standard benchmark functions of various characteristics. The performance of the proposed algorithm is investigated and compared with classical HS, an improved version of HS, the global best HS, self-adaptive HS, explorative HS, and the recently proposed state-of-art gravitational search algorithm. Experimental results reveal that the proposed algorithm outperforms the above-mentioned approaches. The effects of scalability, noise, harmony memory size, and harmony memory consideration rate have also been investigated with the proposed algorithm. The proposed algorithm is then employed for a data clustering problem. Four real-life datasets selected from the UCI machine learning repository have been used. The results indicate that the VHS-based clustering outperforms the existing well-known clustering algorithms.     

Symbiotic organisms search algorithm for dynamic economic dispatch with valve-point effects

Abstract

In this study, symbiotic organisms search (SOS) algorithm is proposed to solve the dynamic economic dispatch with valve-point effects problem, which is one of the most important problems of the modern power system. Some practical constraints like valve-point effects, ramp rate limits and prohibited operating zones have been considered as solutions. Proposed algorithm was tested on five different test cases in 5 units, 10 units and 13 units systems. The obtained results have been compared with other well-known metaheuristic methods reported before. Results show that proposed algorithm has a good convergence and produces better results than other methods.     

An improved bacterial foraging algorithm for combined static/dynamic environmental economic dispatch

Economic dispatch is carried out at the energy control center to find out the optimal output of thermal generating units such that power balance criterion is met, unit operating limits are satisfied and the fuel cost is minimized. With growing environmental awareness and strict government regulations throughout the world, it has become essential to optimize not only the total fuel cost but also the harmful emissions, both, under static as well as dynamic conditions. The static environment economic dispatch finds the optimal output of generating units for a fixed load demand at a given time, while the dynamic environmental economic dispatch schedules the output of online generators with changing power demands over a certain time period (normally one day) so as to minimize these two conflicting objectives, simultaneously. In this paper, the price penalty factor approach is employed for simultaneous minimization of cost and emission. The generator ramp rate constraints, non-convex and discontinuous nature of cost function and the large number of generators in practical power plants, make this problem very difficult to solve. Here, a fuzzy ranking approach is employed to identify the solution which offers the best compromise between cost and emission objectives.     

Economic load dispatch problems with valve-point loading using natural updated harmony search

In this paper, the update process of harmony search (HS) algorithm is modified to improve its concept of diversity. The update process in HS is based on a greedy mechanism in which the new harmony solution, created in each generation, replaces the worst individual in the population, if better. This greedy process could be improved with other updates mechanisms in order to control the diversity perfectly. Three versions of HS have been proposed: (1) Natural Proportional HS ; (2) Natural Tournament HS; (3) Natural Rank HS. These three HS versions employed the natural selection principle of the “survival of the fittest”. Instead of replacing the worst individual in population, any individual can be replaced based on certain criteria. Four versions of economic loading dispatch (ELD) problems with valve point have been used to measure the effect of the newly proposed HS versions. The results show that the new HS versions are very promising for ELD domain. This claim is proved based on the comparative evaluation process where the new HS versions are able to excel the state-of-the-art methods in almost ELD problems used.

     

Distributed fixed step-size algorithm for dynamic economic dispatch with power flow limits

In this study,a discrete-time distributed algorithm is proposed for solving the dynamic economic dispatch problem with active power flow limits and transmission...     

新颖的全局和声搜索算法在经济性调度中的应用

提出采用新颖的全局和声搜索算法来解决经济调度问题,并设计了一种新颖的处理系统约束的方法;介绍了经济调度问题数学模型、新颖的全局和声搜索算法实现过程及其应用方法。实验结果表明,采用新颖的全局和声搜索算法所获得的最优值要明显好于采用进化算法、粒子群算法所获得的最优值,新颖的全局和声搜索算法为解决经济性调度问题提供了一种新的解决方案。     

基于动态惩罚因子的改进蚱蜢算法求解经济负荷调度和经济排放联合调度问题

电力生产装置运行中各种燃料的成本逐步增加,需要最小化成本函数以求解此类复杂经济负荷调度问题.鉴于此,提出一种基于动态惩罚因子的改进蚱蜢算法求解经济负荷调度(economic load dispatch, ELD)问题和经济排放联合调度(combined economic emission dispatch, CEED)问题.为了提高蚱蜢算法(grasshopper optimization algorithm, GOA)性能,提出一种改进的混合蚱蜢算法(hybrid grasshopper optimization algorithm, HGOA),将重力搜索算子和鸽群搜索算子-地标算子加入GOA中,增强算法的搜索能力,平衡算法的勘探和开发.同时,为了更好地解决ELD和CEED问题中的约束问题,提出6个惩罚函数,包括2个V型函数、反正切函数、反正弦函数、线性函数和二次函数,并使用动态惩罚策略代替传统的固定值惩罚策略.选取3个ELD问题案例和4个CEED问题案例验证所提出方法的有效性,实验结果表明, HGOA相较于其他元启发式算法在求解质量上表现更好,且动态惩罚策略比固定值惩罚策略效果更...     

Reserve-constrained multiarea environmental/economic dispatch based on particle swarm optimization with local search

The objective of economic dispatch (ED) is to minimize the total operational cost while satisfying the operational constraints of power systems. Multiarea economic dispatch (MAED) deals with the optimal power dispatch of multiple areas. In this investigation, multiarea environmental/economic dispatch (MAEED) is proposed to address the environmental issue during the ED. Its target is to dispatch the power among different areas by simultaneously minimizing the operational costs and pollutant emissions. In this paper, the MAEED problem is first formulated and then an improved multiobjective particle swarm optimization (MOPSO) algorithm is developed to derive a set of Pareto-optimal solutions. In the proposed version of MOPSO, local search is used to increase its search efficiency. To ensure the system security, tie-line transfer limits between different areas are incorporated as a set of constraints in the optimization process. Moreover, the reserve-sharing scheme is applied to ensure that each area is able to fulfill its reserve requirement. Numerical studies based on a four-area test power generation system are carried out to demonstrate the validity of the proposed optimization method as well as the results from different problem formulations. Comparative results with respect to other optimization methods are also presented.     

随机交叉全局和声搜索算法

针对和声搜索算法易陷入局部最优的不足,提出了一种随机交叉全局和声搜索（RCGHS）算法。通过最差和声向最优和声学习提高算法的全局搜索性能,引入其他和声向最优和声学习的交互策略提高算法的局部搜索性能。将两种学习策略随机交叉动态产生新和声,平衡算法的全局搜索和局部搜索性能。在和声记忆库更新阶段,利用即兴创作产生的和声向量与随机反向学习产生的和声向量中较优的个体更新和声记忆库。将RCGHS算法与目前文献中较优的几种改进HS算法、ABC算法、PSO算法和GWO算法进行性能测试,测试结果表明RCGHS算法具有较高的寻优精度和较快的收敛速度。     

基于极限动态规划算法的微电网一体化调度与控制

随着电力电子技术的发展,微电网已成为分布式发电的必然趋势.传统的多时间尺度控制策略之间的配合使用已经很难同时满足高品质频率稳定控制和经济调度的要求.为解决此问题,本文提出极限动态规划算法.所提算法以自适应动态规划算法为框架,以极限学习机作为其评价模块、模型模块、执行模块、预测模块的内核.基于所提算法的微电网一体化调控控制器能替代传统模式下"下垂控制+自动发电控制+经济调度"多时间尺度控制组合策略.最后,为验证所提算法的有效性,在5个节点的微电网模型进行仿真,结果验证了所提极限动态规划算法的可行性和有效性.     

Modified neo-fuzzy neuron-based approach for economic and environmental optimal power dispatch

At the central energy management center in a power system, the real time controls continuously track the load changes and endeavor to match the total power demand with total generation in such a manner that the operating cost is minimized while all the operating constraints are satisfied. However, due to the strict government regulations on environmental protection, operation at minimum cost is no longer the only criterion for dispatching electrical power. The idea behind the environmentally constrained economic dispatch formulation is to estimate the optimal generation schedule of generating units in such a manner that fuel cost and harmful emission levels are both simultaneously minimized for a given load demand. Conventional optimization techniques become very time consuming and computationally extensive for such complex optimization tasks. These methods are hence not suitable for on-line use. Neural networks and fuzzy systems can be trained to generate accurate relations among variables in complex non-linear dynamical environment, as both are model-free estimators. The existing synergy between these two fields has been exploited in this paper for solving the economic and environmental dispatch problem on-line. A multi-output modified neo-fuzzy neuron (NFN), capable of real time training is proposed for economic and environmental power generation allocation.This model is found to achieve accurate results and the training is observed to be faster than other popular neural networks. The proposed method has been tested on medium-sized sample power systems with three and six generating units and found to be suitable for on-line combined environmental economic dispatch (CEED).     

Fuzzy based fast dynamic programming solution of unit commitment with ramp constraints

Abstract: A fast dynamic programming technique based on a fuzzy based unit selection procedure is proposed in this paper for the solution of the unit commitment problem with ramp constraints. The curse of dimensionality of the dynamic programming technique is eliminated by minimizing the number of prospective solution paths to be stored at each stage of the search procedure. Heuristics like priority ordering of the units, unit grouping, fast economic dispatch based on priority ordering, and avoidance of repeated economic dispatch through memory action have been employed to make the algorithm fast. The proposed method produced comparable results with the best performing methods found in the literature.     

多目标粒子群算法的动态多燃料经济环境负荷分配

考虑动态的负荷需求和多种燃料资源,以经济成本和环境成本为优化指标,建立动态多燃料经济环境负荷分配的多目标优化模型,并提出一种多目标粒子群优化算法求解该类优化模型.模型采用动态负荷需求和多种燃料资源,更有利于节约电能成本和提高能源利用效率,但高维数、复杂非线性和多目标成为求解该优化模型的难点,故在算法中引入多目标解集更新策略和变邻域搜索策略.实验仿真结果表明,该模型是有效的,且采用所提算法求解这类模型时所获得的近似Pareto前端的精度明显优于其他算法.     

Firefly Algorithm for solving non-convex economic dispatch problems with valve loading effect

The growing costs of fuel and operation of power generating units warrant improvement of optimization methodologies for economic dispatch (ED) problems. The practical ED problems have non-convex objective functions with equality and inequality constraints that make it much harder to find the global optimum using any mathematical algorithms. Modern optimization algorithms are often meta-heuristic, and they are very promising in solving nonlinear programming problems. This paper presents a novel approach to determining the feasible optimal solution of the ED problems using the recently developed Firefly Algorithm (FA). Many nonlinear characteristics of power generators, and their operational constraints, such as generation limitations, prohibited operating zones, ramp rate limits, transmission loss, and nonlinear cost functions, were all contemplated for practical operation. To demonstrate the efficiency and applicability of the proposed method, we study four ED test systems having non-convex solution spaces and compared with some of the most recently published ED solution methods. The results of this study show that the proposed FA is able to find more economical loads than those determined by other methods. This algorithm is considered to be a promising alternative algorithm for solving the ED problems in practical power systems.     

Economic dispatch with generation constraints

The classical procedure for solving the economic dispatch problem in the presence of upper and lower limits on the generation levels may fail to lead to the constrained optimum generation schedule. In this paper a simple scheme suitable for real-time applications which resolves this drawback is presented. When transmission losses are neglected, the constrained optimum can be analytically computed based on a distance measure of the unconstrained optimum schedule to the violated limits. In the presence of transmission losses, the problem is first converted into an equivalent lossless case by a simple transformation which can then be solved by the proposed algorithm.     

Modified shuffled frog leaping algorithm with genetic algorithm crossover for solving economic load dispatch problem with valve-point effect

This paper addresses a hybrid solution methodology involving modified shuffled frog leaping algorithm (MSFLA) with genetic algorithm (GA) crossover for the economic load dispatch problem of generating units considering the valve-point effects. The MSFLA uses a more dynamic and less stochastic approach to problem solving than classical non-traditional algorithms, such as genetic algorithm, and evolutionary programming. The potentiality of MSFLA includes its simple structure, ease of use, convergence property, quality of solution, and robustness. In order to overcome the defects of shuffled frog leaping algorithm (SFLA), such as slow searching speed in the late evolution and getting trapped easily into local iteration, MSFLA with GA cross-over is put forward in this paper. MSFLA with GA cross-over produces better possibilities of getting the best result in much less global as well as local iteration as one has strong local search capability while the other is good at global search. This paper proposes a new approach for solving economic load dispatch problems with valve-point effect where the cost function of the generating units exhibits non-convex characteristics, as the valve-point effects are modeled and imposed as rectified sinusoid components. The combined methodology and its variants are validated for the following four test systems: IEEE standard 30 bus test system, a practical Eastern Indian power grid system of 203 buses, 264 lines, and 23 generators, and 13 and 40 thermal units systems whose incremental fuel cost function take into account the valve-point loading effects. The results are quite promising and effective compared with several benchmark methods.     

Large scale economic dispatch of power systems using oppositional invasive weed optimization

This paper presents an evolutionary hybrid algorithm of invasive weed optimization (IWO) merged with oppositional based learning to solve the large scale economic load dispatch (ELD) problems. The oppositional invasive weed optimization (OIWO) is based on the colonizing behavior of weed plants and empowered by quasi opposite numbers. The proposed OIWO methodology has been developed to minimize the total generation cost by satisfying several constraints such as generation limits, load demand, valve point loading effect, multi-fuel options and transmission losses. The proposed algorithm is tested and validated using five different test systems. The most important merit of the proposed methodology is high accuracy and good convergence characteristics and robustness to solve ELD problems. The simulation results of the proposed OIWO algorithm show its applicability and superiority when compared with the results of other tested algorithms such as oppositional real coded chemical reaction, shuffled differential evolution, biogeography based optimization, improved coordinated aggregation based PSO, quantum-inspired particle swarm optimization, hybrid quantum mechanics inspired particle swarm optimization, modified shuffled frog leaping algorithm with genetic algorithm, simulated annealing based optimization and estimation of distribution and differential evolution algorithm.     

A primary unit commitment approach with a modification process

This paper introduces an approach to one of the most important problems in electrical power system called the Unit Commitment (UC). The proposed method PUC-MP which stands for the primary unit commitment-modification process, addresses this problem firstly by using a simple and new priority for operating the generating units in each hour, and then, using a modification process which enhances the solution quality with lower cost. The PUC-MP takes advantage of both deterministic and stochastic algorithms in its structure to solve the discrete-variable part of the UC problem for choosing a suitable combination of units in each hour, and also, continuous-variable part of it which is dispatching the operating units’ output power to the power network load economically. The latter part which is called economic dispatch (ED) has been solved using an intelligent algorithm which in turn has been customized by two new ideas to increase its efficiency. Simulation results show that this new approach even without using its modification process can be considered as an effective approach which surpasses some other popular and recently reported methods in producing near-optimal and robust solutions.     

Nonconvex economic load dispatch using an efficient real-coded genetic algorithm

An efficient optimisation procedure based on real-coded genetic algorithm (RCGA) is proposed for the solution of economic load dispatch (ELD) problem with continuous and nonsmooth/nonconvex cost function and with various constraints being considered. The effectiveness of the proposed algorithm has been demonstrated on different systems considering the transmission losses and valve point loading effect in thermal units. The proposed algorithm is equipped with an effective constraint handling technique, which eliminates the need for penalty parameters. For the purpose of comparison, the same problem has also been solved using binary-coded genetic algorithm (BCGA) and three other popular RCGAs. In the proposed RCGA, simulated binary crossover and polynomial mutation are used against the single point crossover and bit-flipping mutation in BCGA. It has been observed from the test results that the proposed RCGA is more efficient in terms of thermal cost minimisation and execution time for ELD problem with continuous search space than BCGA and some other popular RCGAs.